None of what you said contradicts what I said.

Unemployment insurance generally has a limit (even if the risk you are trying to insure against is not). Is that limit within the reasonable bounds of self insurance? Probably so for many people, but maybe not for others.

Insurance is good for the really huge stuff, like giant medical bills or a house fire. For little stuff, there are so many risks that if something happens, it's probably not listed on whatever policies that you do have.